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complex.t
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complex.t
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#!./parrot
# Copyright (C) 2001-2010, Parrot Foundation.
# $Id$
=head1 NAME
t/pmc/complex.t - Complex Numbers
=head1 SYNOPSIS
% prove t/pmc/complex.t
=head1 DESCRIPTION
Tests the Complex PMC.
=cut
.sub main :main
.include 'test_more.pir'
.include 'fp_equality.pasm'
.include "iglobals.pasm"
plan(459)
string_parsing()
exception_malformed_string__real_part()
exception_malformed_string__imaginary_part()
exception_malformed_string__missing_plus_or_minus()
test_complex_add()
test_complex_subtract()
test_complex_multiply()
test_complex_divide()
complex_divide_by_zero_Complex()
complex_divide_by_zero_Float()
complex_divide_by_zero_Integer()
get_int_or_num_or_bool()
test_get_keyed()
exception_get_keyed__invalid_string_key()
exception_get_keyed__invalid_numeric_key()
set_int_or_num()
set_keyed()
exception_set_keyed__invalid_key()
test_is_equal()
test_complex_abs()
check_whether_interface_is_done()
instantiate__pasm__i()
instantiate__pir__n()
instantiate__pir__p()
instantiate__pir__s()
test_complex_neg()
test_clone()
test_freeze_thaw()
test_sub()
test_i_sub()
sprintf_with_a_complex()
e_raised_pi_time_i__plus_1_equal_0()
ln_of_complex_numbers()
exp_of_complex_numbers()
sqrt_of_complex_numbers()
sin_of_complex_numbers()
cos_of_complex_numbers()
tan_of_complex_numbers()
cot_of_complex_numbers()
sec_of_complex_numbers()
csc_of_complex_numbers()
asin_of_complex_numbers()
acos_of_complex_numbers()
atan_of_complex_numbers()
acot_of_complex_numbers()
asec_of_complex_numbers()
acsc_of_complex_numbers()
sinh_of_complex_numbers()
cosh_of_complex_numbers()
tanh_of_complex_numbers()
coth_of_complex_numbers()
sech_of_complex_numbers()
csch_of_complex_numbers()
add_using_subclass_of_complex_bug_59630()
# END_OF_TESTS
.end
.macro exception_is( M )
.local pmc exception
.local string message
.get_results (exception)
message = exception['message']
is( message, .M, .M )
.endm
.sub string_parsing
$P0 = new ['Complex']
$P1 = new ['String']
set $P0, "4"
is( $P0, "4+0i", '"4" parsed as 4+0i' )
set $P0, "3.14"
is( $P0, "3.14+0i", '"3.14" parsed as 3.14+0i' )
set $P0, ".5"
is( $P0, "0.5+0i", '".5" parsed as 0.5+0i' )
set $P0, "-13"
is( $P0, "-13+0i", '"-13" parsed as -13+0i' )
set $P0, "-.3"
is( $P0, "-0.3+0i", '"-.3" parsed as -0.3+0i' )
set $P0, "i"
is( $P0, "0+1i", '"i" parsed as 0+1i' )
set $P0, "-i"
is( $P0, "0-1i", '"-i" parsed as 0-1i' )
set $P0, ".3i"
is( $P0, "0+0.3i", '".3i" parsed as 0+0.3i' )
set $P0, "2 + 3i"
is( $P0, "2+3i", '"2 + 3i" parsed as 2+3i' )
set $P0, "4 + 3.5i"
is( $P0, "4+3.5i", '"4 + 3.5i" parsed as 4+3.5i' )
set $P0, "2 + .1 i"
is( $P0, "2+0.1i", '"2 + .1 i" parsed as 2+0.1i' )
set $P0, "10 - i"
is( $P0, "10-1i", '"10 - i" parsed as 10-1i' )
set $P0, "5 - .3i"
is( $P0, "5-0.3i", '"5 - .3i" parsed as 5-0.3i' )
set $P1, "-4-i"
assign $P0, $P1
is( $P0, "-4-1i", '"-4-i" parsed as -4-1i' )
set $P1, "- 20 - .5 i"
assign $P0, $P1
is( $P0, "-20-0.5i", '"- 20 - .5 i" parsed as -20-0.5i' )
set $P1, "-13 +2i"
assign $P0, $P1
is( $P0, "-13+2i", '"-13 +2i" parsed as -13+2i' )
.end
.sub exception_malformed_string__real_part
$P0 = new ['Complex']
push_eh handler
set $P0, "q + 3i"
pop_eh
handler:
.exception_is( "Complex: malformed string" )
.end
.sub exception_malformed_string__imaginary_part
$P0 = new ['Complex']
push_eh handler
set $P0, "1 + ij"
pop_eh
handler:
.exception_is( "Complex: malformed string" )
.end
.sub exception_malformed_string__missing_plus_or_minus
$P0 = new ['Complex']
push_eh handler
set $P0, "1 * i"
pop_eh
handler:
.exception_is( "Complex: malformed string" )
.end
.sub test_complex_add
$P0 = new ['Complex']
$P1 = new ['Complex']
$P2 = new ['Float']
$P3 = new ['Integer']
set $P0, "1 + i"
add $P0, $P0, $P0
is( $P0, "2+2i", '1+i plus 1+i' )
set $P0, "1 - i"
set $P1, "1 + i"
add $P0, $P0, $P1
is( $P0, "2+0i", '1-i plus 1+i' )
is( $P1, "1+1i", '1+i as text is 1+1i' )
set $P0, "-i"
set $P1, "1"
add $P1, $P0, $P1
is( $P0, "0-1i", '-i as text is 0-1i' )
is( $P1, "1-1i", '-i plus 1 is 1-1i' )
set $P0, "2 + i"
set $P2, 3.3
add $P1, $P0, $P2
is( $P1, "5.3+1i", '2+i plus 3.3 is 5.3+1i' )
set $P0, "3 + 5i"
add $P1, $P0, 2
is( $P1, "5+5i", '3+5i plus literal 2 is 5+5i' )
set $P0, "2 + 2i"
add $P1, $P0, -2.0
is( $P1, "0+2i", '2+2i plus literal -2.0 is 0+2i' )
set $P0, "3 + 3i"
set $P3, -3
add $P1, $P0, $P3
is( $P1, "0+3i", '3+3i plus -3 is 0+3i' )
add $P1, $P3, $P0
is( $P1, "0+3i", '-2 plus 3+3i is 0+3i' )
.end
.sub test_complex_subtract
$P0 = new ['Complex']
$P1 = new ['Complex']
$P2 = new ['Float']
$P3 = new ['Integer']
set $P0, "1 + i"
sub $P0, $P0, $P0
is( $P0, "0+0i", '1+i minus 1+i is 0+0i' )
set $P0, "1 - i"
set $P1, "1 + i"
sub $P0, $P0, $P1
is( $P0, "0-2i", '1-i minus 1+i is 0-2i' )
is( $P1, "1+1i", '... original $3 is unchanged' )
set $P0, "-i"
set $P1, "1"
sub $P1, $P0, $P1
is( $P0, "0-1i", '-i minus 1 is 0-1i' )
is( $P1, "-1-1i", '... original $3 is unchanged' )
set $P0, "1 - 4i"
set $P2, -1.0
sub $P1, $P0, $P2
is( $P1, "2-4i", '1-4i minus -1.0 is 2-4i' )
set $P0, "- 2 - 2i"
sub $P1, $P0, -4
is( $P1, "2-2i", '-2-2i minus -4 is 2-2i' )
set $P0, "3 + i"
sub $P1, $P0, 1.2
is( $P1, "1.8+1i", '3+i - literal 1.2 is 1.8+1i' )
set $P0, "1024 - 3i"
set $P3, 2048
sub $P1, $P0, $P3
is( $P1, "-1024-3i", '1024-3i minus 2048 is -1024-3i' )
sub $P1, $P3, $P0
is( $P1, "1024+3i", '2048 minus 1024-3i is 1024+3i' )
.end
.sub test_complex_multiply
$P0 = new ['Complex']
$P1 = new ['Complex']
$P2 = new ['Float']
$P3 = new ['Integer']
set $P0, "2 + 3i"
mul $P0, $P0, $P0
is( $P0, "-5+12i", '2+3i x 2+3i = -5+12i' )
set $P0, "5 - 2i"
set $P1, "5 + 2i"
mul $P0, $P0, $P1
is( $P0, "29+0i", '5-2i x 5+2i = 29+0i' )
is( $P1, "5+2i", '... original $3 is unchanged' )
set $P0, "3i"
set $P1, "2 - i"
mul $P1, $P0, $P1
is( $P0, "0+3i", '3i x 2-i = 0+3i' )
is( $P1, "3+6i", '... original $3 is unchanged' )
set $P0, "2 - 2i"
set $P2, 0.5
mul $P1, $P0, $P2
is( $P1, "1-1i", '2-2i x 0.5 = 1-1i' )
set $P0, "1 - i"
mul $P1, $P0, 2
is( $P1, "2-2i", '1-i x literal 2 = 2-2i' )
set $P0, "-1 + i"
mul $P1, $P0, -1.0
is( $P1, "1-1i", '-1+i x literal -1.0 = 1-1i' )
set $P0, "1 + i"
set $P3, 10
mul $P1, $P0, $P3
is( $P1, "10+10i", '1+i x literal 10 = 10+10i' )
mul $P1, $P3, $P0
is( $P1, "10+10i", '10 x 1+i is 10+10i' )
.end
.sub test_complex_divide
$P0 = new ['Complex']
$P1 = new ['Complex']
$P2 = new ['Float']
set $P0, "2 + 3i"
div $P0, $P0, $P0
is( $P0, "1+0i", '2+3i / 2+3i = 1+0i' )
set $P0, "3 + 5i"
set $P1, "5 - 3i"
div $P0, $P0, $P1
is( $P0, "0+1i", '3+5i / 5-3i = 0+1i' )
is( $P1, "5-3i", '... original $3 is unchanged' )
set $P0, "25"
set $P1, "3 + 4i"
div $P1, $P0, $P1
is( $P1, "3-4i", '25 / 3+4i = 3-4i' )
is( $P0, "25+0i", '... original $2 is unchanged' )
set $P0, "-3 + 6i"
set $P2, 3.0
div $P1, $P0, $P2
is( $P1, "-1+2i", '-3+6i / 3.0 = -1+2i' )
set $P0, "-2 + 3i"
div $P1, $P0, 2
is( $P1, "-1+1.5i", '-2+3i / 2 = -1+1.5i' )
set $P0, "2 - 3i"
div $P1, $P0, 0.5
is( $P1, "4-6i", '2-3i / 0.5 = 4-6i' )
.end
.sub complex_divide_by_zero_Complex
skip( 1, 'div by zero not caught' )
.return()
$P0 = new ['Complex']
set $P0, "4+3.5i"
$P1 = new ['Complex']
## divide by a zero Complex
$P2 = new ['Complex']
set $P2, 0
push_eh handler
$P1 = $P0 / $P2
pop_eh
handler:
.exception_is( 'Divide by zero' )
.end
.sub complex_divide_by_zero_Float
skip( 1, 'div by zero not caught' )
.return()
$P0 = new ['Complex']
set $P0, "4+3.5i"
$P1 = new ['Complex']
## divide by a zero Float
$P2 = new ['Float']
set $P2, 0
push_eh handler
$P1 = $P0 / $P2
handler:
.exception_is( 'Divide by zero' )
.end
.sub complex_divide_by_zero_Integer
skip( 1, 'div by zero not caught' )
.return()
$P0 = new ['Complex']
set $P0, "4+3.5i"
$P1 = new ['Complex']
## divide by a zero Integer
$P2 = new ['Integer']
set $P2, 0
push_eh handler
$P1 = $P0 / $P2
handler:
.exception_is( 'Divide by zero' )
.end
.sub get_int_or_num_or_bool
$P0 = new ['Complex']
set $P0, "2 - 1.5i"
is( $P0, "2-1.5i", 'Complex "2 - 1.5i" returned ok' )
set $I0, $P0
is( $I0, "2", 'Complex -> Int = 2' )
set $N0, $P0
.fp_eq_ok( $N0, 2.5, 'Complex -> Num = 2.5')
ok( $P0, 'Complex(2-1.5i) -> bool = true' )
set $P0, "0"
nok( $P0, 'Complex(0) -> bool = true' )
.end
.sub test_get_keyed
$P0 = new ['Complex']
$P1 = new ['String']
set $P0, "- 3.3 + 1.2i"
set $P1, "imag"
set $N0, $P0["real"]
set $N1, $P0["imag"]
set $N2, $P0[$P1]
.fp_eq_ok( $N0, -3.3, 'got real part')
.fp_eq_ok( $N1, 1.2, 'got imag part')
.fp_eq_ok( $N2, 1.2, 'got imag part using variable' )
set $P2, $P0["real"]
set $P3, $P0[$P1]
is( $P2, "-3.3", 'get real portion of -3.3i1.2i' )
is( $P3, "1.2", 'get imag portion of -3.3+1.2i' )
set $I0, $P0["real"]
set $I1, $P0[$P1]
is( $I0, "-3", 'get real portion -> Int' )
is( $I1, "1", 'get imag portion -> Int' )
.end
.sub exception_get_keyed__invalid_string_key
$P0 = new ['Complex']
set $P0, "5 + 3.5i"
push_eh handler
set $N0, $P0["Foo55"]
handler:
.exception_is( "Complex: key is neither 'real' or 'imag'" )
.end
.sub exception_get_keyed__invalid_numeric_key
$P0 = new ['Complex']
set $P0, "5 + 3.5i"
push_eh handler
set $N0, $P0[2]
handler:
.exception_is( "Complex: key must be 0 or 1" )
.end
.sub set_int_or_num
$P0 = new ['Complex']
set $P0, "3 + 4i"
set $P0, -2
is( $P0, "-2+0i", '-2 -> Complex = -2+0i' )
set $P0, "2 + 5i"
set $P0, .4
is( $P0, "0.4+0i", '.4 -> Complex = 0.4+0i' )
.end
.sub set_keyed
$P0 = new ['Complex']
$P1 = new ['String']
$P2 = new ['String']
set $P1, "real"
set $P0[$P1], 1
set $P0["imag"], 4
is( $P0, "1+4i", 'set imag and real portion separately' )
set $P0[$P1], 3.2
set $P0["imag"], -2.3
is( $P0, "3.2-2.3i", '... again' )
set $P2, ".5"
set $P0[$P1], $P2
set $P2, 6
set $P0["imag"], $P2
is( $P0, "0.5+6i", '... now using String PMCs' )
.end
.sub exception_set_keyed__invalid_key
$P0 = new ['Complex']
push_eh handler
set $P0[2], 12.5
handler:
.exception_is( "Complex: key must be 0 or 1" )
.end
.sub test_is_equal
$P0 = new ['Complex']
$P1 = new ['Complex']
set $P0, "2 + 3j"
set $P1["real"], 2
set $P1["imag"], 3
is( $P0, $P1, 'create new Complex from real/imag and test eq' )
set $P1, 0
isnt( $P0, $P1, '... now make sure it ne to 0' )
.end
.sub test_complex_abs
$P0 = new ['Complex']
set $P0, "4 + 3i"
$P1 = new ['Undef']
abs $P1, $P0
is( $P1, "5", 'abs 4+3j -> 5' )
.end
.sub check_whether_interface_is_done
.local pmc pmc1
pmc1 = new ['Complex']
.local int bool1
does bool1, pmc1, "scalar"
ok( bool1, 'Comples does scalar' )
does bool1, pmc1, "no_interface"
nok( bool1, 'Comples !does no_interface' )
.end
.sub instantiate__pasm__i
skip( 1, 'instantiate n/y' )
.return()
set $I0, 1
set $I1, 2
set $I2, 0
set $I3, 0
set $I4, 0
set $I5, 10
set $I6, 20
get_class $P2, "Complex"
# instantiate $P1
is( $P1, "10+20i", 'instantiate pasm i' )
.end
.sub instantiate__pir__n
skip( 1, 'instantiate n/y' )
.return()
$P0 = get_class "Complex"
# $P1 = $P0."instantiate"(2.0, 3.0)
is( $P1, "2+3i", 'instantiate pir n' )
.end
.sub instantiate__pir__p
skip( 1, 'instantiate n/y' )
.return()
$P0 = get_class "Complex"
$P1 = new ['Float']
$P1 = 2.0
$P2 = new ['Float']
$P2 = 3.0
# $P1 = $P0."instantiate"($P1, $P2)
is( $P1, "2+3i", 'instantiate pir p' )
.end
.sub instantiate__pir__s
skip( 1, 'instantiate n/y' )
.return()
$P0 = get_class "Complex"
# $P1 = $P0."instantiate"("2 + 3i")
is( $P1, "2+3i", 'instantiate pir s' )
.end
.sub test_complex_neg
$P0 = new ['Complex']
set $P0, "1.3 + 1.7i"
$P1 = new ['Integer']
neg $P1, $P0
set $N0, $P1[0]
set $N1, $P1[1]
.fp_eq_ok($N0, -1.3, 'test complex negative')
.fp_eq_ok($N1, -1.7, '... and the imag port')
.end
.sub test_clone
$P0 = new ['Complex']
set $P0, "1 - 3i"
clone $P1, $P0
is( $P0, $P1, 'clone Complex PMC')
set $P0, "0 + 0i"
set $N0, $P1[0]
set $N1, $P1[1]
.fp_eq_ok($N0, 1.0, 'no change to cloned after setting orig')
.fp_eq_ok($N1, -3.0, '... nor to imag portion')
.end
.sub test_freeze_thaw
$P0 = new ['Complex']
set $P0, "1 - 3i"
$S0 = freeze $P0
$P1 = thaw $S0
is($P0, $P1, 'roundtrip serialize Complex PMC')
.end
.sub test_sub
.local pmc d, f, c
d = new ['Undef']
f = new ['Float']
c = new ['Complex']
f = 2.2
c = "5+2j"
d = c - f
is( d, "2.8+2i", '5+2j - 2.2 = 2.8+i (using d=c-f)' )
typeof $S0, d
is( $S0, "Complex", 'd is typeof Complex' )
d = f - c
is( d, "-2.8-2i", '2.2 - 5+2j = -2.8-2i' )
typeof $S0, d
is( $S0, "Complex", 'typeof still Complex' )
.end
.sub test_i_sub
.local pmc f, c
f = new ['Float']
f = 2.2
c = new ['Complex']
c = "5+2j"
c -= f
is( c, '2.8+2i', 'Complex -= test' )
c = new ['Complex']
c = "5+2j"
f -= c
is( f, '-2.8-2i', '... and reverse it' )
.end
.macro sprintf_is(fmt, number, message)
c = .number
$S0 = sprintf .fmt, c
$S1 = .message
is( $S0, $S1, $S1 )
.endm
.sub sprintf_with_a_complex
.local pmc c, c2
c = new ['Complex']
.sprintf_is( "%d%+di", "1.35+35.1i", "1+35i" )
.sprintf_is( "%.3f%+.3fi", "0+3.141592653589793i", "0.000+3.142i" )
.sprintf_is( "%.3f%+.3fi", "0+i", "0.000+1.000i" )
.end
.sub e_raised_pi_time_i__plus_1_equal_0
.local pmc c, c2, c3
c = new ['Complex']
c2 = new ['Complex']
c3 = new ['Complex']
# e^(pi * i) + 1 = 0
$N0 = atan 1
$N0 *= 4
c[0] = 0.0
c[1] = $N0
c2 = c.'exp'()
c2 += 1.0
.sprintf_is( "%.3f%+.3fi", c2, "0.000+0.000i" )
.end
# # The inverse hyperbolic functions are broken wrt -0.0
# # Need to find some formal spec for when to return -0.0.
.macro complex_op_is( val, res, op )
$P1 = new ['Complex']
$P2 = new ['Complex']
set $P1, .val
set $S0, .val
set $S1, .res
set $S2, .op
#XXX: can't do $P1.'$S2'()
$P2 = $P1. $S2()
$S3 = sprintf "%f%+fi", $P2
concat $S4, $S2, " of "
concat $S4, $S4, $S0
is( $S3, $S1, $S4 )
.endm
.macro complex_op_todo( val, res, op, todo )
$P1 = new ['Complex']
$P2 = new ['Complex']
set $P1, .val
set $S0, .val
set $S1, .res
set $S2, .op
set $S3, .todo
#XXX: can't do $P1.'$S2'()
$P2 = $P1. $S2()
$S3 = sprintf "%f%+fi", $P2
concat $S5, $S2, " of "
concat $S5, $S5, $S4
$I0 = cmp_str $S1, $S3
$I0 = not $I0
todo( $I0, $S4 )
.endm
.sub ln_of_complex_numbers
.complex_op_is("-2+0i", "0.693147+3.141593i", 'ln' )
.complex_op_is("-1+0i", "0.000000+3.141593i", 'ln' )
.complex_op_is("-0.5+0i", "-0.693147+3.141593i", 'ln' )
.complex_op_is("0.5+0i", "-0.693147+0.000000i", 'ln' )
.complex_op_is("1+0i", "0.000000+0.000000i", 'ln' )
.complex_op_is("2+0i", "0.693147+0.000000i", 'ln' )
.complex_op_is("0-2i", "0.693147-1.570796i", 'ln' )
.complex_op_is("0-1i", "0.000000-1.570796i", 'ln' )
.complex_op_is("0-0.5i", "-0.693147-1.570796i", 'ln' )
.complex_op_is("0+0.5i", "-0.693147+1.570796i", 'ln' )
.complex_op_is("0+1i", "0.000000+1.570796i", 'ln' )
.complex_op_is("0+2i", "0.693147+1.570796i", 'ln' )
t_inf:
skip(1, 'inf is not platform-independent' )
goto end_inf
.complex_op_is("0+0i", "-inf+0.000000i", 'ln' )
end_inf:
.complex_op_is("2+3i", "1.282475+0.982794i", 'ln' )
.complex_op_is("2-3i", "1.282475-0.982794i", 'ln' )
.complex_op_is("-2+3i", "1.282475+2.158799i", 'ln' )
.complex_op_is("-2-3i", "1.282475-2.158799i", 'ln' )
.end
.sub exp_of_complex_numbers
.complex_op_is( "-2+0i", "0.135335+0.000000i", 'exp' )
.complex_op_is( "-1+0i", "0.367879+0.000000i", 'exp' )
.complex_op_is( "-0.5+0i", "0.606531+0.000000i", 'exp' )
.complex_op_is( "0.5+0i", "1.648721+0.000000i", 'exp' )
.complex_op_is( "1+0i", "2.718282+0.000000i", 'exp' )
.complex_op_is( "2+0i", "7.389056+0.000000i", 'exp' )
.complex_op_is( "0-2i", "-0.416147-0.909297i", 'exp' )
.complex_op_is( "0-1i", "0.540302-0.841471i", 'exp' )
.complex_op_is( "0-0.5i", "0.877583-0.479426i", 'exp' )
.complex_op_is( "0+0.5i", "0.877583+0.479426i", 'exp' )
.complex_op_is( "0+1i", "0.540302+0.841471i", 'exp' )
.complex_op_is( "0+2i", "-0.416147+0.909297i", 'exp' )
.complex_op_is( "0+0i", "1.000000+0.000000i", 'exp' )
.complex_op_is( "2+3i", "-7.315110+1.042744i", 'exp' )
.complex_op_is( "2-3i", "-7.315110-1.042744i", 'exp' )
.complex_op_is( "-2+3i", "-0.133981+0.019099i", 'exp' )
.complex_op_is( "-2-3i", "-0.133981-0.019099i", 'exp' )
.end
.sub sqrt_of_complex_numbers
.complex_op_is( "4", "2.000000+0.000000i", 'sqrt' )
.complex_op_is( "i", "0.707107+0.707107i", 'sqrt' )
.complex_op_is( "2i","1.000000+1.000000i", 'sqrt' )
.complex_op_is( "2+2i", "1.553774+0.643594i", 'sqrt' )
.complex_op_is( "1+i", "1.098684+0.455090i", 'sqrt' )
.complex_op_is( "-2+0i", "0.000000+1.414214i", 'sqrt' )
.complex_op_is( "-1+0i", "0.000000+1.000000i", 'sqrt' )
.complex_op_is( "-0.5+0i", "0.000000+0.707107i", 'sqrt' )
.complex_op_is( "0.5+0i", "0.707107+0.000000i", 'sqrt' )
.complex_op_is( "1+0i", "1.000000+0.000000i", 'sqrt' )
.complex_op_is( "2+0i", "1.414214+0.000000i", 'sqrt' )
.complex_op_is( "0-2i", "1.000000-1.000000i", 'sqrt' )
.complex_op_is( "0-1i", "0.707107-0.707107i", 'sqrt' )
.complex_op_is( "0-0.5i", "0.500000-0.500000i", 'sqrt' )
.complex_op_is( "0+0.5i", "0.500000+0.500000i", 'sqrt' )
.complex_op_is( "0+1i", "0.707107+0.707107i", 'sqrt' )
.complex_op_is( "0+2i", "1.000000+1.000000i", 'sqrt' )
.complex_op_is( "0+0i", "0.000000+0.000000i", 'sqrt' )
.complex_op_is( "2+3i", "1.674149+0.895977i", 'sqrt' )
.complex_op_is( "2-3i", "1.674149-0.895977i", 'sqrt' )
.complex_op_is( "-2+3i", "0.895977+1.674149i", 'sqrt' )
.complex_op_is( "-2-3i", "0.895977-1.674149i", 'sqrt' )
.end
.sub sin_of_complex_numbers
.complex_op_is("-2+0i", "-0.909297+0.000000i", 'sin' )
.complex_op_is("-1+0i", "-0.841471+0.000000i", 'sin' )
.complex_op_is("-0.5+0i", "-0.479426+0.000000i", 'sin' )
.complex_op_is("0.5+0i", "0.479426+0.000000i", 'sin' )
.complex_op_is("1+0i", "0.841471+0.000000i", 'sin' )
.complex_op_is("2+0i", "0.909297+0.000000i", 'sin' )
.complex_op_is("0-2i", "0.000000-3.626860i", 'sin' )
.complex_op_is("0-1i", "0.000000-1.175201i", 'sin' )
.complex_op_is("0-0.5i", "0.000000-0.521095i", 'sin' )
.complex_op_is("0+0.5i", "0.000000+0.521095i", 'sin' )
.complex_op_is("0+1i", "0.000000+1.175201i", 'sin' )
.complex_op_is("0+2i", "0.000000+3.626860i", 'sin' )
.complex_op_is("0+0i", "0.000000+0.000000i", 'sin' )
.complex_op_is("2+3i", "9.154499-4.168907i", 'sin' )
.complex_op_is("2-3i", "9.154499+4.168907i", 'sin' )
.complex_op_is("-2+3i", "-9.154499-4.168907i", 'sin' )
.complex_op_is("-2-3i", "-9.154499+4.168907i", 'sin' )
.end
.sub cos_of_complex_numbers
.complex_op_is("-2+0i", "-0.416147+0.000000i", 'cos' )
.complex_op_is("-1+0i", "0.540302+0.000000i", 'cos' )
.complex_op_is("-0.5+0i", "0.877583+0.000000i", 'cos' )
.complex_op_is("0.5+0i", "0.877583+0.000000i", 'cos' )
.complex_op_is("1+0i", "0.540302+0.000000i", 'cos' )
.complex_op_is("2+0i", "-0.416147+0.000000i", 'cos' )
.complex_op_is("0-2i", "3.762196+0.000000i", 'cos' )
.complex_op_is("0-1i", "1.543081+0.000000i", 'cos' )
.complex_op_is("0-0.5i", "1.127626+0.000000i", 'cos' )
.complex_op_is("0+0.5i", "1.127626+0.000000i", 'cos' )
.complex_op_is("0+1i", "1.543081+0.000000i", 'cos' )
.complex_op_is("0+2i", "3.762196+0.000000i", 'cos' )
.complex_op_is("0+0i", "1.000000+0.000000i", 'cos' )
.complex_op_is("2+3i", "-4.189626-9.109228i", 'cos' )
.complex_op_is("2-3i", "-4.189626+9.109228i", 'cos' )
.complex_op_is("-2+3i", "-4.189626+9.109228i", 'cos' )
.complex_op_is("-2-3i", "-4.189626-9.109228i", 'cos' )
.end
.sub tan_of_complex_numbers
.complex_op_is("-2+0i", "2.185040+0.000000i", 'tan' )
.complex_op_is("-1+0i", "-1.557408+0.000000i", 'tan' )
.complex_op_is("-0.5+0i", "-0.546302+0.000000i", 'tan' )
.complex_op_is("0.5+0i", "0.546302+0.000000i", 'tan' )
.complex_op_is("1+0i", "1.557408+0.000000i", 'tan' )
.complex_op_is("2+0i", "-2.185040+0.000000i", 'tan' )
.complex_op_is("0-2i", "0.000000-0.964028i", 'tan' )
.complex_op_is("0-1i", "0.000000-0.761594i", 'tan' )
.complex_op_is("0-0.5i", "0.000000-0.462117i", 'tan' )
.complex_op_is("0+0.5i", "0.000000+0.462117i", 'tan' )
.complex_op_is("0+1i", "0.000000+0.761594i", 'tan' )
.complex_op_is("0+2i", "0.000000+0.964028i", 'tan' )
.complex_op_is("0+0i", "0.000000+0.000000i", 'tan' )
.complex_op_is("2+3i", "-0.003764+1.003239i", 'tan' )
.complex_op_is("2-3i", "-0.003764-1.003239i", 'tan' )
.complex_op_is("-2+3i", "0.003764+1.003239i", 'tan' )
.complex_op_is("-2-3i", "0.003764-1.003239i", 'tan' )
.end
.sub cot_of_complex_numbers
.complex_op_is("-2+0i", "0.457658+0.000000i", 'cot' )
.complex_op_is("-1+0i", "-0.642093+0.000000i", 'cot' )
.complex_op_is("-0.5+0i", "-1.830488+0.000000i", 'cot' )
.complex_op_is("0.5+0i", "1.830488+0.000000i", 'cot' )
.complex_op_is("1+0i", "0.642093+0.000000i", 'cot' )
.complex_op_is("2+0i", "-0.457658+0.000000i", 'cot' )
.complex_op_is("0-2i", "0.000000+1.037315i", 'cot' )
.complex_op_is("0-1i", "0.000000+1.313035i", 'cot' )
.complex_op_is("0-0.5i", "0.000000+2.163953i", 'cot' )
.complex_op_is("0+0.5i", "0.000000-2.163953i", 'cot' )
.complex_op_is("0+1i", "0.000000-1.313035i", 'cot' )
.complex_op_is("0+2i", "0.000000-1.037315i", 'cot' )
.complex_op_is("2+3i", "-0.003740-0.996758i", 'cot' )
.complex_op_is("2-3i", "-0.003740+0.996758i", 'cot' )
.complex_op_is("-2+3i", "0.003740-0.996758i", 'cot' )
.complex_op_is("-2-3i", "0.003740+0.996758i", 'cot' )
.end
.sub sec_of_complex_numbers
.complex_op_is("-2+0i", "-2.402998+0.000000i", 'sec' )
.complex_op_is("-1+0i", "1.850816+0.000000i", 'sec' )
.complex_op_is("-0.5+0i", "1.139494+0.000000i", 'sec' )
.complex_op_is("0.5+0i", "1.139494+0.000000i", 'sec' )
.complex_op_is("1+0i", "1.850816+0.000000i", 'sec' )
.complex_op_is("2+0i", "-2.402998+0.000000i", 'sec' )
.complex_op_is("0-2i", "0.265802+0.000000i", 'sec' )
.complex_op_is("0-1i", "0.648054+0.000000i", 'sec' )
.complex_op_is("0-0.5i", "0.886819+0.000000i", 'sec' )
.complex_op_is("0+0.5i", "0.886819+0.000000i", 'sec' )
.complex_op_is("0+1i", "0.648054+0.000000i", 'sec' )
.complex_op_is("0+2i", "0.265802+0.000000i", 'sec' )
.complex_op_is("0+0i", "1.000000+0.000000i", 'sec' )
.complex_op_is("2+3i", "-0.041675+0.090611i", 'sec' )
.complex_op_is("2-3i", "-0.041675-0.090611i", 'sec' )
.complex_op_is("-2+3i", "-0.041675-0.090611i", 'sec' )
.complex_op_is("-2-3i", "-0.041675+0.090611i", 'sec' )
.end
.sub csc_of_complex_numbers
.complex_op_is("-2+0i", "-1.099750+0.000000i", 'csc' )
.complex_op_is("-1+0i", "-1.188395+0.000000i", 'csc' )
.complex_op_is("-0.5+0i", "-2.085830+0.000000i", 'csc' )
.complex_op_is("0.5+0i", "2.085830+0.000000i", 'csc' )
.complex_op_is("1+0i", "1.188395+0.000000i", 'csc' )
.complex_op_is("2+0i", "1.099750+0.000000i", 'csc' )
.complex_op_is("0-2i", "0.000000+0.275721i", 'csc' )
.complex_op_is("0-1i", "0.000000+0.850918i", 'csc' )
.complex_op_is("0-0.5i", "0.000000+1.919035i", 'csc' )
.complex_op_is("0+0.5i", "0.000000-1.919035i", 'csc' )
.complex_op_is("0+1i", "0.000000-0.850918i", 'csc' )
.complex_op_is("0+2i", "0.000000-0.275721i", 'csc' )
.complex_op_is("2+3i", "0.090473+0.041201i", 'csc' )
.complex_op_is("2-3i", "0.090473-0.041201i", 'csc' )
.complex_op_is("-2+3i", "-0.090473+0.041201i", 'csc' )
.complex_op_is("-2-3i", "-0.090473-0.041201i", 'csc' )
.end
.sub asin_of_complex_numbers
.complex_op_is("-2+0i", "-1.570796+1.316958i", 'asin' )
.complex_op_is("-1+0i", "-1.570796+0.000000i", 'asin' )
.complex_op_is("-0.5+0i", "-0.523599+0.000000i", 'asin' )
.complex_op_is("0.5+0i", "0.523599+0.000000i", 'asin' )
.complex_op_is("1+0i", "1.570796+0.000000i", 'asin' )
.complex_op_is("2+0i", "1.570796-1.316958i", 'asin' )
.complex_op_is("0-2i", "0.000000-1.443635i", 'asin' )
.complex_op_is("0-1i", "0.000000-0.881374i", 'asin' )
.complex_op_is("0-0.5i", "0.000000-0.481212i", 'asin' )
.complex_op_is("0+0.5i", "0.000000+0.481212i", 'asin' )
.complex_op_is("0+1i", "0.000000+0.881374i", 'asin' )
.complex_op_is("0+2i", "0.000000+1.443635i", 'asin' )
.complex_op_is("0+0i", "0.000000+0.000000i", 'asin' )
.complex_op_is("2+3i", "0.570653+1.983387i", 'asin' )
.complex_op_is("2-3i", "0.570653-1.983387i", 'asin' )
.complex_op_is("-2+3i", "-0.570653+1.983387i", 'asin' )
.complex_op_is("-2-3i", "-0.570653-1.983387i", 'asin' )
.end
.sub acos_of_complex_numbers
.complex_op_is("-2+0i", "3.141593-1.316958i", 'acos' )
.complex_op_is("-1+0i", "3.141593+0.000000i", 'acos' )
.complex_op_is("-0.5+0i", "2.094395+0.000000i", 'acos' )
.complex_op_is("0.5+0i", "1.047198+0.000000i", 'acos' )
.complex_op_is("1+0i", "0.000000+0.000000i", 'acos' )
.complex_op_is("2+0i", "0.000000+1.316958i", 'acos' )
.complex_op_is("0-2i", "1.570796+1.443635i", 'acos' )
.complex_op_is("0-1i", "1.570796+0.881374i", 'acos' )
.complex_op_is("0-0.5i", "1.570796+0.481212i", 'acos' )
.complex_op_is("0+0.5i", "1.570796-0.481212i", 'acos' )
.complex_op_is("0+1i", "1.570796-0.881374i", 'acos' )
.complex_op_is("0+2i", "1.570796-1.443635i", 'acos' )
.complex_op_is("0+0i", "1.570796+0.000000i", 'acos' )
.complex_op_is("2+3i", "1.000144-1.983387i", 'acos' )
.complex_op_is("2-3i", "1.000144+1.983387i", 'acos' )
.complex_op_is("-2+3i", "2.141449-1.983387i", 'acos' )
.complex_op_is("-2-3i", "2.141449+1.983387i", 'acos' )
.end
.sub atan_of_complex_numbers
.complex_op_is("-2+0i", "-1.107149+0.000000i", 'atan' )
.complex_op_is("-1+0i", "-0.785398+0.000000i", 'atan' )
.complex_op_is("-0.5+0i", "-0.463648+0.000000i", 'atan' )
.complex_op_is("0.5+0i", "0.463648+0.000000i", 'atan' )
.complex_op_is("1+0i", "0.785398+0.000000i", 'atan' )
.complex_op_is("2+0i", "1.107149+0.000000i", 'atan' )
.complex_op_is("0-2i", "-1.570796-0.549306i", 'atan' )
.complex_op_is("0-0.5i", "0.000000-0.549306i", 'atan' )
.complex_op_is("0+0.5i", "0.000000+0.549306i", 'atan' )
.complex_op_is("0+2i", "-1.570796+0.549306i", 'atan' )
.complex_op_is("0+0i", "0.000000+0.000000i", 'atan' )
.complex_op_is("2+3i", "1.409921+0.229073i", 'atan' )
.complex_op_is("2-3i", "1.409921-0.229073i", 'atan' )
.complex_op_is("-2+3i", "-1.409921+0.229073i", 'atan' )
.complex_op_is("-2-3i", "-1.409921-0.229073i", 'atan' )
.end
.sub acot_of_complex_numbers
.complex_op_is("-2+0i", "-0.463648+0.000000i", 'acot' )
.complex_op_is("-1+0i", "-0.785398+0.000000i", 'acot' )
.complex_op_is("-0.5+0i", "-1.107149+0.000000i", 'acot' )
.complex_op_is("0.5+0i", "1.107149+0.000000i", 'acot' )
.complex_op_is("1+0i", "0.785398+0.000000i", 'acot' )
.complex_op_is("2+0i", "0.463648+0.000000i", 'acot' )
.complex_op_is("0-2i", "0.000000+0.549306i", 'acot' )
.complex_op_is("0-0.5i", "-1.570796+0.549306i", 'acot' )
.complex_op_is("0+0.5i", "-1.570796-0.549306i", 'acot' )
.complex_op_is("0+2i", "0.000000-0.549306i", 'acot' )
.complex_op_is("2+3i", "0.160875-0.229073i", 'acot' )
.complex_op_is("2-3i", "0.160875+0.229073i", 'acot' )
.complex_op_is("-2+3i", "-0.160875-0.229073i", 'acot' )
.complex_op_is("-2-3i", "-0.160875+0.229073i", 'acot' )
.end
.sub asec_of_complex_numbers
.complex_op_is("-2+0i", "2.094395+0.000000i", 'asec' )
.complex_op_is("-1+0i", "3.141593+0.000000i", 'asec' )
.complex_op_is("-0.5+0i", "3.141593-1.316958i", 'asec' )
.complex_op_is("0.5+0i", "0.000000+1.316958i", 'asec' )
.complex_op_is("1+0i", "0.000000+0.000000i", 'asec' )
.complex_op_is("2+0i", "1.047198+0.000000i", 'asec' )
.complex_op_is("0-2i", "1.570796-0.481212i", 'asec' )
.complex_op_is("0-1i", "1.570796-0.881374i", 'asec' )
.complex_op_is("0-0.5i", "1.570796-1.443635i", 'asec' )
.complex_op_is("0+0.5i", "1.570796+1.443635i", 'asec' )
.complex_op_is("0+1i", "1.570796+0.881374i", 'asec' )
.complex_op_is("0+2i", "1.570796+0.481212i", 'asec' )
.complex_op_is("2+3i", "1.420411+0.231335i", 'asec' )
.complex_op_is("2-3i", "1.420411-0.231335i", 'asec' )
.complex_op_is("-2+3i", "1.721182+0.231335i", 'asec' )
.complex_op_is("-2-3i", "1.721182-0.231335i", 'asec' )
.end
.sub acsc_of_complex_numbers
.complex_op_is("-2+0i", "-0.523599+0.000000i", 'acsc' )
.complex_op_is("-1+0i", "-1.570796+0.000000i", 'acsc' )
.complex_op_is("-0.5+0i", "-1.570796+1.316958i", 'acsc' )
.complex_op_is("0.5+0i", "1.570796-1.316958i", 'acsc' )
.complex_op_is("1+0i", "1.570796+0.000000i", 'acsc' )
.complex_op_is("2+0i", "0.523599+0.000000i", 'acsc' )
.complex_op_is("0-2i", "0.000000+0.481212i", 'acsc' )